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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Convergence of conditional expectations and strong laws of large numbers for multivalued random variables

Author: Fumio Hiai
Journal: Trans. Amer. Math. Soc. 291 (1985), 613-627
MSC: Primary 60F15; Secondary 60B12
MathSciNet review: 800254
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Abstract: Fatou’s lemmas and Lebesgue’s convergence theorems are established for multivalued conditional expectations of random variables having values in the closed subsets of a separable Banach space. Strong laws of large numbers are also given for such multivalued random variables.

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Keywords: Multivalued random variable, Mosco convergence, conditional expectation, Fatou’s lemma, Lebesgue’s convergence theorem, strong law of large numbers
Article copyright: © Copyright 1985 American Mathematical Society